1. Field of the Invention
This invention relates to apparatus and methods for forming a phase conjugate mirror, and more particularly to phase conjugate mirrors employing a photorefractive material as the conjugating medium.
2. Description of the Prior Art
Phase conjugation is an optical phenomenon that has attracted considerable attention in recent years. Several different ways of producing phase conjugated beams have been discussed in the literature, including four-wave mixing, stimulated Brillouin scattering, Raman scattering, three-wave mixing and photon echo devices. A review of various applications of optical phase conjugation is presented by Giuliano in Physics Today, "Application of Optical Phase Conjugation", April 1981, pages 27-35. A general review of the field is given in A. Yariv, IEEE, J. Quantum Electronics QE14, 650 (1978), and R. Fisher, "Optical Phase Conjugation", Academic Press, N.Y., 1983.
Basically, a phase conjugate mirror PCM produces a retro-reflective reflection of an incident beam, with the sign of the phase of the reflected beam reversed from that of the incident beam at the point of reflection. A typical PCM known in the prior art is shown in FIG. 1. This is illustrated as a four-wave mixer, in which a pair of contradirectional laser beams 2 and 4 are directed into an optical mixing medium 6. A probe laser beam E.sub.I, equal in frequency to beams 2 and 4, is directed into the mixing medium from the side. As a result of the action of the various beams within the mixing medium, a reflected beam RE.sub.I *, where R is the coefficient of reflectivity, is reflected back in a direction opposite to incident beam E.sub.I. Since power is pumped into the system by beams 2 and 4, the reflector may produce an amplification which makes R greater than 1. In addition to being retro-reflective to the incident beam, the phase conjugated reflected beam also undergoes a phase reversal with respect to the incident beam at the point of reflection.
PCMs can be provided either with external pumping beams, as in the four-wave mixer illustrated in FIG. 1, or as a "self-pumped" device, the advantage of the self-pumped variety residing in the elimination of the requirement for external pump beams. Of the self-pumped PCMs, those employing Brillouin or Raman scattering are generally employed in connection with high power pulsed laser beams, such as from a Nd:YAG laser, but do not work with low power lasers such as HeNe. Another type of self-pumped PCM is based upon the use of a photorefractive material with a large electro-optic coefficient as the phase conjugating medium.
It will be helpful at this point to briefly discuss the characteristics which distinguish photorefractive materials. In general, a photorefractive material is one in which the index of refraction changes under the influence of applied light, such as a laser beam. The light causes charges within the photorefractive material to migrate and separate, producing an internal electrostatic field. This field produces a change in the crystal's refractive index by the linear electro-optic effect (the Pockels effect). The photorefractive "index grating", or periodic variation in the crystal's index of refraction, is a measure of the change in the index.
The formation of a photorefractive index grating is illustrated in FIG. 2, in which the horizontal axis represents distance along the normal to the grating formed by the interference of two beams within the photorefractive crystal. The upper graph illustrates the pattern of light with a spatially periodic intensity I within the crystal, while the next graph illustrates the resulting charge density .rho. within the crystal. The mobile charges, illustrated as being of positive polarity, tend to accumulate in the dark regions of the light intensity pattern. The resulting periodic charge distribution produces a periodic electrostatic field E by Poisson's equation. This electric field, illustrated in the third graph of FIG. 2, then causes a change in the refractive index .DELTA.N of the crystal by the linear electro-optic effect. This photorefractive effect, illustrated in the last graph of FIG. 2, is non-local in that the maximum refractive index change does not occur at the peak of the light intensity. In FIG. 2 the spatial shift between .DELTA.N and I is 1/4 of the grating period, corresponding to a 90.degree. phase shift.
Typical photorefractive materials are LiNbO.sub.3, KNbO.sub.3, BaTiO.sub.3, SBN, Bi.sub.12 SiO.sub.20, Bi.sub.12 TiO.sub.20, Bi.sub.12 GeO.sub.20, GaAs and InP. Other materials with a non-zero electro-optic coefficient and a large donor-trap population are expected to be photorefractive. Only a small number of photorefractive materials, with electro-optic coefficients substantially greater than 10 picometers/volt, have been found to be capable of producing an inherently self-pumped PCM. Photorefractive materials with electro-optic coefficients in the order of 10 picometers/volt or less have been found to exhibit insufficient gain to support a self-pumped operation.
Self-pumped PCMs using BaTiO.sub.3 (barium titanate) and Sn.sub.1-x Ba.sub.x Nb.sub.2 O.sub.6 (strontium barium niobate) have previously been demonstrated (White et al., Appl. Phys. Lett. 40, p. 450, (1982); Feinberg, Opt. Lett. 7, 486, (1982)). The theory of the electro-optic effect is described in a text by A. Yariv, "Introduction to Optical Electronics, 2d ed.", pp. 246-53 (1976). The largest electro-optic coefficient is BaTiO.sub.3 is 1640 pm/V. These materials, however, have several drawbacks. They are difficult to obtain in good optical quality and large sizes, operate in relatively small temperture ranges (BaTiO.sub.3 has a destructive phase transition at 5.degree. C.), have a relatively slow responsive time, and are not sensitive at all wavelengths of interest. One wavelength range to which these materials are not particularly sensitive, but which is very important for several commercial applications, is the range of about 0.7 microns to about 11 microns; commercial applications within this range include optical data processing, beam combining, adaptive optics, photolithography and others.
Several years after publication of the White et al. and Feinberg papers, a series of papers were published by Stepanov and Petrov in which the use of photorefractive materials for both phase conjugation and holography was discussed (Optics Communications 53, 292, Apr. 1, 1985; Proc. of ICO-13, Sapporo 1984; Sov. Tech. Phys. Lett. 10 (11), November 1984). These papers developed the concept of applying an alternating electric field to a photorefractive material to increase its two-wave mixing gain coefficient for holographic and image processing applications. This was suggested as an improvement over prior uses of photorefractive materials for holography and image processing, in which a DC electric field had been employed to increase the gain of the material. Stepanov and Petrov thus reported improved results from an alternating field but, in the very same papers in which they disclosed the use of an alternating field for two-wave holography, they suggested a continuation of the four-wave external pumping arrangement for phase conjugation. No suggestion was made for the realization of a self-pumped PCM.